A variational theory for finite-step elasto-plastic problems

Abstract

An extended version ofgeneralized standard elasto-plastic material is considered in the framework of an internal variable theory of associated plasticity. According to a backward difference scheme for time integration of the flow rule, a finite-step structural problem is formulated in a geometrically linear range. Convex analysis and a brand new potential theory for monotone multivalued operators are shown to provide the natural mathematical setting for the derivation of the related variational formulation. A general stationarity principle is obtained and then specialized to obtain a minimum principle in terms of displacements, plastic strains and internal variables. A critical comparison with an analogous minimum principle recently proposed in literature is performed, showing the inadequacy of classical procedures in deriving non-smooth variational formulations.